Questions tagged [computational-physics]

Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists.

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1answer
52 views

Sum of random variables - Check your derived distribution against a numerical calculation/histogram

Consider independent random variates $X_0, X_1, . . .$ each uniformly distributed on the support $[0, 1)$ Let's say $Y = X_0 + X_1$, where $X_0$ and $X_1$ are independent uniform random variables with ...
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1answer
90 views

Trouble Making 3rd-Order Sympletic Integrator for Planitary N-Body Problem (A Hamiltonian System)

I am doing a solar-system simulation. I am using Ruth's 3rd order sympletic integrator to avoid the problem of Energy Drift (which I had with RK4), but the the planets quickly leave orbit, and energy ...
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25 views

Negative binomial expansion of general symbolic polynomial

Using Sympy, I would like to compute the negative binomial expansion of a general symbolic polynomial, e.g., $(x_1 + x_2 + x_3 + 4 x_4)^{-1}$. I understand that I can go by recursively partitioning ...
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Problems with simulation of a spatial filter 4f setup (Python)

I have a question about my code which computes numerically the output field of a 4f setup with a pinhole in the middle which works as a spatial filter. My setup consists of two lenses with 50mm focal ...
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1answer
676 views

Help with Fourier beam propagation method

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...
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0answers
72 views

More efficient way to calculate magnetic field using Biot-Savart

I am writing a program in python that is supposed to calculate the magnetic field along a conducting coil that is made up of a bunch of points, and the magnetic field is generated by other conducting ...
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3answers
320 views

Finite-difference software for solving custom equations

Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as ...
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1answer
59 views

Why is Time evolving block decimation so efficient?

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
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18answers
9k views

Good examples of “two is easy, three is hard” in computational sciences

I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows: When a certain problem is ...
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1answer
410 views

1-D turbulent energy spectra in homogeneous direction (non-isotropic)

I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
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1answer
40 views

Getting streamline for a lid driven cavity flow in openFoam/ParaView

I have installed openFoam on Debian GNU/Linux and learning from official user guide. I have a problem with generating streamlines. I am trying to generate streamlines as explained in the post ...
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Set of integrators do not consistently solve an equation in Python

I must solve the following second order differential equation: $\delta \phi^{''}_{\mathbf{k}}+(3-\epsilon)\delta \phi^{'}_{\mathbf{k}}+\left(\frac{k^2}{a^2 H^2}+\frac{V_{,\phi\phi}}{H^2}-6\epsilon +4\...
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Calypso with quantum espresso for nanoparticles

Any one uses Calypso structure prediction? http://www.calypso.cn/documentation/ I want to run a two type molecules nanoparticle structure Any suggestions will be helpfull. Or if any other tools for ...
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1answer
113 views

Why is $1/r^2$ force law giving spiral trajectory?

I have written a program to solve for Newton's 2nd Law of motion for a given force law, in 2D polar coordinates. It is known that if the force law is of the form $k/r^2$,we get conic sections as ...
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2answers
106 views

Optimization of expensive model with many parameters

I have a physical model which takes $\sim50$ parameters and gives $\sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs as close as possible to data. ...
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1answer
95 views

Calculating the Strange Attractor of the Duffing Oscillator in C++

I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working through Thijssen's ...
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3answers
118 views

Numerically finding constants of motion

Given a set of ODE's $ \dot{z} = f(z) $ (or discrete time $ z_{t+1} = f(z_t) $), is there a way to numerically find constants of motion? For $ f(z_t) \approx M z_t $, diagonalizing the matrix $ M $ ...
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1answer
126 views

coupled equations with finite difference method

I have these three differential equations in which I need to solve numerically: $$ \frac{dn_0}{dt}= -n_0(t)W_{01}(t) + n_1(t)K_{10} $$ $$ \frac{dn_1}{dt}= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(t)K_{...
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1answer
1k views

Conserving Energy in Physics Simulation with imperfect Numerical Solver

I am creating a C++ Physics Simulation where I need to move an rigid body through an acting force field. Problem: simulation does not conserve energy. Quesiton: abstractly, how is conservation of ...
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20 views

Hawkes Process : recursive formula for : $R'_{m,n} (k) = \sum_{ \{i : t_i^n < t_k^m \} } (t_k^m - t_i^n) \exp ( - \beta_{m,n} ( t_k^m - t_i^n ) ) $

Following the advice of a fellow mathematician, I am asking my question here from (https://mathoverflow.net/questions/365554/hawkes-process-recursive-formula-for-r-m-n-k-sum-i-t-in-t) I need to use a ...
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1answer
61 views

Plotting the difference between an exponential and its Taylor expansion as a function of number of terms?

I'm terribly green, please forgive me. I need to plot the difference between a chosen calculated Taylor expansion $e^x=1+x+\frac {x^2}{2!}+\frac {x^3}{3!}+\frac {x^4}{4!}+\frac {x^5}{5!}$... and the ...
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1answer
56 views

Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC). Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm. We have at the ...
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0answers
52 views

Choosing good modelling method for solving Boltzmann equation

I'm writing a solver for Boltzmann Equations (BE) including a force term in rarefied plasma, for my PhD. The aim is to see if an instability occurs inside an electric streamer (theoretically it should,...
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1answer
92 views

Calculate stable time step DG method for advection-diffusion

For stable time steps for the RKDG method for transport equations we require that $$ \Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|}, $$ where $\lambda$ is the eigenvalue of our conservation law ...
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1answer
385 views

General case Kutta condition

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
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1answer
58 views

Solving an ODE using odeint in Python and continuing the integration

The following relates to the linked question: Scattering of waves in a symmetrical potential (using python) I have attempted to solve the problem for $U(r)$ using ...
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1answer
63 views

Effect on methods like Crank-Nicolson of adding a potential term, changing heat equation to Schrodinger equation

I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...
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0answers
107 views

Propagation of a Gaussian beam using FFT

I am trying to simulate the propagation of a gaussian beam through a lens using an FFT approach. I tried to implement the approach described by Couairon in this paper at page 43: https://link....
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30 views

COMSOL Circularl polarization

I'm having some problems trying to implement circularly polarized light in COMSOL Muliphysics. For a isotropic homogenous media, I've obtained without problems the TE and TM reflectance curves. ...
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1answer
34 views

MATLAB ode45 doesn't start at initial conditions

I wrote a code in MATLAB to solve a system of differential equations, but my solution doesn't seem to take into consideration the initial conditions I specified. I am not sure how to interpret this ...
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0answers
22 views

How to plot a function for multiple values of a parameter in the same set of axes in Python?

I'm currently trying to plot a graph wich describes a photoionization cross section as a function of incident photon energy for optical transition in a semiconductor for different values of the $\...
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1answer
68 views

Applications of Julia in Chemistry and Molecular Physics?

I was wondering if there are any Theoretical & Computational Chemistry (MM, QM) codes or publications out there that are based primarily on the Julia programming language?
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3answers
4k views

Calculating partial trace of array in NumPy

A simulation I'm doing requires me to calculate the partial trace of a large density matrix. I am trying to calculate it using tools from numpy, but my code seems to be having some problems. For ...
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1answer
136 views

Numerical calculation of Wannier function in optical lattice

I am working out some optical lattice band structures (example here). I have no issue with setting up the eigenvalue equation: $$ H_{jj'}c_{j'}=Ec_{j'} $$ Where $H$ is the tri-diagonal matrix that ...
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1answer
91 views

Applying weak form

I have two dimensional equation and I want to solve it using Finite Element Methods. $$ \nabla . (\alpha(x,y)\nabla u(x,y)) + \dfrac{\partial u(x,y)}{\partial x}+\dfrac{\partial u(x,y)}{\partial y}+u(...
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64 views

Applying boundary Conditions on FEM

I have a partial differential equatons as shown below. $$\dfrac{d}{dx}((1+x)\dfrac{du(x)}{dx})=0$$ With the following boundary conditions. $$u(0)=0, u(3)=10$$ To solve it using FEM, I multiplied the ...
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1answer
125 views

Scattering of waves in a symmetrical potential (using python)

I'm looking at scattering of waves in a symmetrical potential as part of a research project. If a plane wave $e^{(ikr)}$ is incident on a spherically symmetric potential $V(r)$ the scattered wave is ...
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39 views

Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps

I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ...
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1answer
114 views

Difference between MoM and FEM

Method of Moments and Finite Element Methods are two of the most used methods in computational electromagnetics to solve electromagnetic equations. As it is known, in FEM sparse matrixes are used ...
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2answers
141 views

Solving a Boundary Value Question $\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$ using Python

I'm looking to solve this boundary value question using the shooting method! $$\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$$ given the initial values: $$y'(x=-1)=-1\\y'(x=5)=0$$ I'm aware of ...
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4answers
239 views

In Matlab, how can I be consistent with units?

I am modeling some aerodynamics equations and am using meters / centimeters, kilograms, and seconds. I've heard that, "matlab doesn't know units". So, how can I make sure that it does? Just ...
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0answers
51 views

Lattice spring models vs. finite element models

I am a beginning graduate student in the field of continuum mechanics. It is my understanding that most problems in this field are numerically solved via finite element methods (FEM). However, I have ...
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0answers
29 views

Tackling multiscale problem in numerical simulation

In a dusty plasma system there are more than one component with different masses, i.e, electrons, ions,neutrals and dust grains. Accordingly, there are more than one temporal and spatial scales ...
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1answer
60 views

Is this behaviour normal for a Lennard-Jones monte carlo simulation?

I am simulating a Lennard-Jones fluid using MC simulation. The code always uses a reduced unit. I want to find the potential energy of the system. Periodic boundary condition implemented. I have ...
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0answers
54 views

Why this LJ molecular dynamics result doesn't converge?

I am doing a molecular dynamics simulation of Leonard Jones 6-12 potential. But instead of converging to a particular value. It always stays between -5.58 to -5.62. The standard value is -5.517. The ...
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1answer
57 views

How long should the hyperelastic equations be solved before updating the mesh?

How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid: $$ \nabla\cdot\sigma + f = \rho\ddot{...
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1answer
43 views

Numpys `tensordot` and what is happening mathematically

I've encountered a program where np.tensordot was used, so I tried looking it up but I can't really understand what this function is doing... I feel rather ...
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1answer
52 views

How to get free energy surface of a 3d Ising Spin system using Monte Carlo simulation?

I am doing a Monte Carlo Simulation of the properties of a 3D Ising Spin system. I want to get the free energy surface of the spin system from the simulation. It is a magnetization vs free energy ...
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1answer
79 views

Why the magnetisation shows abrupt behaviour for this 3D ising spin system

I am trying to simulate a 3D Ising spin system (+1 & -1) using Monte Carlo Metropolis Algorithm. I want to get different physical quantities from this simulation like magnetization, Average Energy,...
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1answer
151 views

Absence of Discontinuity in Specific Heat Plot Simulated by Ising Model

I am working on 2D Ising model, when I plot "specific heat vs temperature", I can't see any discontinuity at critical temperature around Tc ~ 2.7K. I am enclosing results of all other thermodynamic ...

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